We need to simplify the expression by first converting all the fractions to a common denominator.

4/21 + (13/4 - 11/12) - 5/14 + 2/3

To find the common denominator, we can use the least common multiple of the denominators: 21, 4, 12, and 14, which is 84.

So, we can rewrite the expression with a common denominator of 84:

(16/84) + ((273/84) - (77/84)) - (30/84) + (56/84)

Now we can simplify:

16/84 + (273/84 - 77/84) - 30/84 + 56/84
16/84 + (196/84) - 30/84 + 56/84
16/84 + 196/84 - 30/84 + 56/84
(16 + 196 - 30 + 56)/84
238/84
119/42

Therefore, the simplified expression is 119/42.